Here's a good calendar of the overall schedule. You can shoot your M1 in just about any highpower rifle match (except those specific to other rifles, such as the Springfield M1A Match), but the one you probably would like most is the John C. Garand Match on August 7th.

Here's the CMP National Matches page, and here's the NRA National Matches page. In short, the CMP matches are first, and the NRA matches come next. There are pistol, smallbore, and highpower rifle matches. Check the schedules for the various dates of each.

This will give you some idea of the size of the National Garand Match - it's huge.